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arXiv:2410.04382 · The European Physical Journal A

Inclusion of pairing fluctuations in a semiclassical approach: the case of study of the Josephson effect

V. Piselli, L. Pisani, Giancarlo Calvanese Strinati

Published Mar 5, 2024• 1 citation
arXivHTMLPDF
DOI
10.1140/epja/s10050-024-01258-x

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Most theoretical treatments of inhomogeneous superconductivity/fermionic superfluidity have been based on the Bogoliubov-deGennes equations (or, else, on their various simplified forms), which implement a standard mean-field decoupling in the presence of spatial inhomogeneities. This approach is reliable even at finite temperature for weak interparticle attraction, when the Cooper pair size is much larger than the average interparticle distance (corresponding to the BCS limit of the BCS-BEC crossover). However, it loses accuracy for increasing attraction when the Cooper pair size becomes comparable or even smaller than the average interparticle distance (corresponding to the BEC limit of the BCS-BEC crossover), in particular when finite-temperature effects are considered. In these cases, inclusion of pairing fluctuations beyond mean field is required, a task that turns out to be especially difficult in the presence of inhomogeneities. Here, we implement the inclusion of pairing fluctuations directly on a coarse-graining version of the Bogoliubov-deGennes equations, which makes it simpler and faster to obtain a solution over the whole sector of the temperature-coupling phase diagram of the BCS-BEC crossover in the broken-symmetry phase. We apply this method in the presence of a supercurrent flow, such that problems related to the Josephson effect throughout the BCS-BEC crossover can be addressed under a variety of circumstances. This is relevant in the view of recent experimental data with ultracold Fermi atoms, to which the results of the present approach are shown to favorably compare in the companion paper.
A realistic description of the Josephson effect at finite temperature with ultracold Fermi gases embedded in nontrivial geometrical constraints (typically, a trap plus a barrier) requires appropriate consideration of pairing fluctuations that arise in inhomogeneous environments. Here, we apply the theoretical approach developed in a companion paper [Pisani et al., Phys. Rev. B 108, 214503 (2023)], where the inclusion of pairing fluctuations beyond mean field across the BCS--Bose-Einstein-condensate (BEC) crossover at finite temperature is combined with a detailed description of the gap parameter in a nontrivial geometry. In this way, we are able to account for the experimental results on the Josephson critical current, reported both at low temperature for various couplings across the BCS-BEC crossover and as a function of temperature at unitarity. Besides validating the theoretical approach of the companion paper, our numerical results reveal generic features of the Josephson effect which may not readily emerge from an analysis of corresponding experiments with condensed-matter samples owing to the unique intrinsic flexibility of experiments with ultracold gases.
A realistic description of the Josephson effect at finite temperature with ultra-cold Fermi gases embedded in nontrivial geometrical constraints (typically, a trap plus a barrier) requires appropriate consideration of pairing fluctuations that arise in inhomogeneous environments. Here, we apply the theoretical approach developed in the companion article [Pisani \emph{et al.}, Phys. Rev. B {\bf 108}, 214503 (2023)], where the inclusion of pairing fluctuations beyond mean field across the BCS-BEC crossover at finite temperature is combined with a detailed description of the gap parameter in a nontrivial geometry. In this way, we are able to account for the experimental results on the Josephson critical current, reported both at low temperature for various couplings across the BCS-BEC crossover and as a function of temperature at unitarity. Besides validating the theoretical approach of the companion article, our numerical results reveal generic features of the Josephson effect which may not readily emerge from an analysis of corresponding experiments with condensed-matter samples owing to the unique intrinsic flexibility of experiments with ultra-cold gases.